Then, motivated by [1]}, [2]}, [3]}, we propose to solve a TV norm-penalized approximation of (REF ), as
\(x^* = \arg \min \limits _{x:=[x_i]} ~ \sum _{i \in \mathcal {R}} \bigg ( \mathbb {E}[F(x_i, \xi _i)] + \frac{\lambda }{2} \sum _{j \in \mathcal {R}_i} \Vert x_i - x_j \Vert _1 + f_0(x_i)\bigg ),\) 
